Details

sample293.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 75.012213%

Space saved by search: 75.012213%

Guaranteed chance to sample good point: 99.804688%

Results

197.0ms	29×	body	640	valid
22.0ms	44×	body	1280	valid
11.0ms	157×	body	80	valid
5.0ms	256×	pre	80	true
5.0ms	22×	body	320	valid
1.0ms	4×	body	160	valid

simplify384.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	6
1	18	6
2	21	6
3	22	6
4	22	6

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
0.1b	(* e (sin v))
0.1b	(* e (cos v))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`associate-r` `associate-l`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l*`

Counts

3 → 59

Calls

3 calls:

6.0ms	(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
4.0ms	(* e (sin v))
6.0ms	(* e (cos v))

series44.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
7.0ms	(* e (sin v))
16.0ms	(* e (cos v))

simplify41.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	295	396
1	1372	344
2	5001	344

prune95.0ms

Filtered

48 candidates to 68 candidates (-41.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	5	69

Merged error: 0.0b

Counts

69 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* e (cos v))
0.1b	(/ (+ 1.0 (* e (cos v))) (sin v))
0.2b	(/ e (/ (+ 1.0 (* e (cos v))) (sin v)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
57×	`add-sqr-sqrt`
55×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
12×	`add-exp-log` `add-cbrt-cube`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-r` `associate-l` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`flip3-+` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 117

Calls

3 calls:

4.0ms	(* e (cos v))
5.0ms	(/ (+ 1.0 (* e (cos v))) (sin v))
7.0ms	(/ e (/ (+ 1.0 (* e (cos v))) (sin v)))

series43.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* e (cos v))
15.0ms	(/ (+ 1.0 (* e (cos v))) (sin v))
22.0ms	(/ e (/ (+ 1.0 (* e (cos v))) (sin v)))

simplify64.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	518	1298
1	2327	1224
2	5002	1224

prune160.0ms

Filtered

101 candidates to 126 candidates (-24.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	125	6	131

Merged error: 0.0b

Counts

131 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* e (cos v))
0.1b	(/ (+ 1.0 (* e (cos v))) (sin v))
0.3b	(/ (sqrt e) (/ (/ (+ 1.0 (* e (cos v))) (sin v)) (sqrt e)))
0.3b	(/ (/ (+ 1.0 (* e (cos v))) (sin v)) (sqrt e))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

1566×	`times-frac`
742×	`add-sqr-sqrt`
740×	`add-cube-cbrt` `*-un-lft-identity`
564×	`sqrt-prod`
91×	`associate-/r*`
59×	`div-inv`
22×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
10×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `associate-r` `associate-l` `clear-num` `associate-/l/`
1×	`flip3-+` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 756

Calls

4 calls:

7.0ms	(* e (cos v))
5.0ms	(/ (+ 1.0 (* e (cos v))) (sin v))
27.0ms	(/ (sqrt e) (/ (/ (+ 1.0 (* e (cos v))) (sin v)) (sqrt e)))
9.0ms	(/ (/ (+ 1.0 (* e (cos v))) (sin v)) (sqrt e))

series75.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* e (cos v))
15.0ms	(/ (+ 1.0 (* e (cos v))) (sin v))
28.0ms	(/ (sqrt e) (/ (/ (+ 1.0 (* e (cos v))) (sin v)) (sqrt e)))
26.0ms	(/ (/ (+ 1.0 (* e (cos v))) (sin v)) (sqrt e))

simplify165.0ms

Algorithm

egg-herbie

Counts

768 → 768

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2327	14946
1	5001	14415

prune703.0ms

Filtered

385 candidates to 768 candidates (-99.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	767	1	768
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	768	6	774

Merged error: 0b

Counts

774 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt e) (+ 1.0 (* e (cos v))))
0.1b	(* e (cos v))
0.2b	(* (sqrt e) (sin v))
0.3b	(* (/ (sqrt e) (+ 1.0 (* e (cos v)))) (* (sqrt e) (sin v)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
37×	`add-cube-cbrt` `*-un-lft-identity`
36×	`times-frac`
33×	`associate-l`
25×	`sqrt-prod`
22×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
8×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
6×	`associate-/l*`
5×	`pow-prod-down`
4×	`associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/r` `-commutative` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`frac-2neg` `associate-*l/` `clear-num`

Counts

4 → 125

Calls

4 calls:

5.0ms	(/ (sqrt e) (+ 1.0 (* e (cos v))))
4.0ms	(* e (cos v))
5.0ms	(* (sqrt e) (sin v))
11.0ms	(* (/ (sqrt e) (+ 1.0 (* e (cos v)))) (* (sqrt e) (sin v)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (sqrt e) (+ 1.0 (* e (cos v))))
7.0ms	(* e (cos v))
15.0ms	(* (sqrt e) (sin v))
27.0ms	(* (/ (sqrt e) (+ 1.0 (* e (cos v)))) (* (sqrt e) (sin v)))

simplify100.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	757	1264
1	3821	1122
2	5002	1119

prune146.0ms

Filtered

98 candidates to 137 candidates (-39.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	137	6	143

Merged error: 0b

Counts

143 → 6

regimes166.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

end0.0ms

sample2.1s

Algorithm

intervals

sampling

Space saved by range analysis: 75.012213%

Space saved by search: 75.012213%

Guaranteed chance to sample good point: 99.804688%

Results

767.0ms	1552×	body	1280	valid
395.0ms	1278×	body	640	valid
299.0ms	4235×	body	80	valid
151.0ms	634×	body	320	valid
149.0ms	8000×	pre	80	true
49.0ms	301×	body	160	valid

Details

sample293.0ms

simplify384.0ms

prune5.0ms

localize13.0ms

rewrite19.0ms

series44.0ms

simplify41.0ms

prune95.0ms

localize10.0ms

rewrite21.0ms

series43.0ms

simplify64.0ms

prune160.0ms

localize12.0ms

rewrite112.0ms

series75.0ms

simplify165.0ms

prune703.0ms

localize12.0ms

rewrite30.0ms

series74.0ms

simplify100.0ms

prune146.0ms

regimes166.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling